Question: All of the 3rd grade teachers and students from Oak went on a field trip to an archaeology museum. Tickets were $$5.50$ each for teachers and $$3.50$ each for students, and the group paid $$57.00$ in total. A few weeks later, the same group visited a natural history museum where the tickets cost $$11.00$ each for teachers and $$9.00$ each for students, and the group paid $$134.00$ in total. Find the number of teachers and students on the field trips.
Explanation: Let $x$ equal the number of teachers and $y$ equal the number of students. The system of equations is: ${5.5x+3.5y = 57}$ ${11x+9y = 134}$ Solve for $x$ and $y$ using elimination. Multiply the top equation by $-2$ ${-11x-7y = -114}$ ${11x+9y = 134}$ Add the top and bottom equations together. $ 2y = 20 $ $ y = \dfrac{20}{2}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $ {5.5x+3.5y = 57}$ to find $x$ ${5.5x + 3.5}{(10)}{= 57}$ $5.5x+35 = 57$ $5.5x = 22$ $x = \dfrac{22}{5.5}$ ${x = 4}$ You can also plug ${y = 10}$ into $ {11x+9y = 134}$ and get the same answer for $x$ ${11x + 9}{(10)}{= 134}$ ${x = 4}$ There were $4$ teachers and $10$ students on the field trips.